Why do you think Petruchio compliments Kate, even when he is telling her what to do in Act III Scene II of The Taming of the Shrew?"But for my bonny, Kate, she must be with me."

This is an interesting question to consider. We need to take this quote in context and realise that this is Petruchio's most important moment in his attempt to "tame" his shrew of a wife. She has just defied him publicly when he said that he and his wife must leave that night when she said:

For me, I'll not be gone till I please myself.

'Tis like you'll prove a jolly surly groom,

That take...

This is an interesting question to consider. We need to take this quote in context and realise that this is Petruchio's most important moment in his attempt to "tame" his shrew of a wife. She has just defied him publicly when he said that he and his wife must leave that night when she said:

For me, I'll not be gone till I please myself.

'Tis like you'll prove a jolly surly groom,

That take it on you at the first so roundly.

The audience excitedly anticipate a true fight as the bride and groom get used to the ways of each other, yet Petruchio simply restates his command that Katharina go with him. Perhaps the compliment is there to soften the bitter pill of his authority, or perhaps he is being sarcastic (he has been so before). The text does not make it clear, however, just after he calls his wife "bonny," he makes it evidently clear, addressing both his wife and the guests, that now she is married to him, she is considered his property:

Nay, look not big, nor stamp, nor stare, nor fret;

I will be master of what is mine own.

She is my goods, my chattels; she is my house,

My household stuff, my field, my barn,

My horse, my ox, my ass, my anything;

And here she stands, touch her whoever dare.

This is a very famous quote from the play that talks about the rights of man and how they "own" the women they are married to. This is an authority that cannot be argued against, as Kate discovers as her husband and Lord shames and humilates her into submissiveness.